Final answer:
To determine the matrix representation of a linear transformation, the transformation of each basis vector is needed. The question provides the transformation of the first basis vector, but additional information is required to complete the matrix.
Step-by-step explanation:
To determine the matrix representation of the linear transformation T from ℝ³ to ℝ³, we need to know how T transforms the standard basis vectors of ℝ³. The given information states that T([1, 0, 0]) = [1, 3, -2]. This implies that the first column of the matrix representation of T is [1, 3, -2].
However, we also need to know T([0, 1, 0]) and T([0, 0, 1]) for the second and third columns of the matrix. If we are only given T([1, 0, 0]), we cannot determine the complete matrix representation of T without additional information about how T acts on the other basis vectors of ℝ³.
It's important to note that the question asked doesn't provide enough data. For a full matrix representation, the transformations of the other basis vectors, like T([0, 1, 0]) and T([0, 0, 1]), are required.